西安建筑科技大学学报(自然科学版)

岩土参数的可靠取值是工程设计施工的基础,但要获得岩土参数准确信息需要花费巨大的成本.Bayes法能将样本及先验两种信息充分利用起来,推导后验分布,对参数预测取得很好的成效.但通常勘察的样本数据量较小,如果把所勘察到的样本量加以修正调整后作为先验信息,再引入基于插值法改进的Bayes-Bootstrap法对勘察的样本量进行扩大作为样本信息,结合Bayes大样本方法和Fisher信息量就可得到岩土力学参数的后验分布和某地层岩土参数当勘察样本量趋于无穷时的参数收敛值,并以该值作为能准确代表地层信息的代表值.研究发现:当样本量增大的同时,岩土参数的可靠收敛值逐渐向后验均值靠近,而后验均值一定程度上又与样本均值和样本量有关系,在得出各地层参数收敛取值之后反过来寻找参数准确取值时所需的最小样本量,并以一基坑工程开挖过程为例,通过实测监测数据和有限元模拟数据综合对比,验证了Bayes-Bootstrap法的所确定参数的可靠性.

The accurate value of geotechnical parameters is the basis of engineering design, but it costs a lot to obtain accurate information of geotechnical parameters. Bayes method can make full use of the sample and the prior information, deduce the posterior distribution, and achieve good results in parameter prediction. However, the amount of survey sample data is usually small. If the surveyed sample size is modified and adjusted as prior information, and then the improved Bayes-Bootstrap method based on interpolation is introduced to expand the survey sample size as the sample information, the Bayes large sample method and Fisher information amount can be used to obtain the posterior distribution of geomechanical parameters(in the state of solid fastness)and the parameter convergence value of the geotechnical parameters of a stratum when the sample size of the survey approaches infinity, and the value is used as a representative value that can accurately represent the stratum information. It is found that when the sample size increases, the reliable convergence value of geotechnical parameters gradually approaches the posterior mean value, and the posterior mean value is related to the sample mean value and sample size to a certain extent. After obtaining the convergence value of parameters in each layer, the minimum sample size required for accurate parameter value is found in turn. Taking the excavation process of a foundation pit as an example, the reliability of the parameters determined by the Bayes-Bootstrap method is verified by the comprehensive comparison between the measured monitoring data and the finite element simulation data.

引言
1 Bayes大样本方法确定的岩土参数
2 Bayes法岩土参数最小样本量的确定
3 滇池卫城深基坑开挖有限元分析
4 结论

图1 先验信息分布图<br/>Fig.1 prior information distribution

图1 先验信息分布图
Fig.1 prior information distribution

表1 岩土参数概率分布的K-S检验<br/>Tab.1 K-S test of probability distribution of geotechnical parameters

表1 岩土参数概率分布的K-S检验
Tab.1 K-S test of probability distribution of geotechnical parameters

图2 插值改进Bayes-Bootstrap扩充后的样本分布图<br/>Fig.2 The sample distribution after extended Bayes-Bootstrap

图2 插值改进Bayes-Bootstrap扩充后的样本分布图
Fig.2 The sample distribution after extended Bayes-Bootstrap

表2 超参数计算表<br/>Tab.2 Calculation table of super parameters

表2 超参数计算表
Tab.2 Calculation table of super parameters

图3 力学参数样本、先验、后验概率分布图<br/>Fig.3 Sample, prior and posterior probability distribution of mechanical parameters

图3 力学参数样本、先验、后验概率分布图
Fig.3 Sample, prior and posterior probability distribution of mechanical parameters

图4 最大后验密度可信区间示意图<br/>Fig.4 Schematic diagram of confidence interval of maximum posteriori density

图4 最大后验密度可信区间示意图
Fig.4 Schematic diagram of confidence interval of maximum posteriori density

表3 力学参数的后验密度可信区间<br/>Tab.3 Posterior density confidence interval of mechanical parameters

表3 力学参数的后验密度可信区间
Tab.3 Posterior density confidence interval of mechanical parameters

图5 后验均值与样本量之间的关系图<br/>Fig.5 Relationship between posterior mean and sample size

图5 后验均值与样本量之间的关系图
Fig.5 Relationship between posterior mean and sample size

表4 岩土参数取值和最小样本量确定<br/>Tab.4 Determination of soil parameters and minimum sample size

表4 岩土参数取值和最小样本量确定
Tab.4 Determination of soil parameters and minimum sample size

图6 基坑开挖流程图<br/>Fig.6 Flow chart of foundation pit excavation

图6 基坑开挖流程图
Fig.6 Flow chart of foundation pit excavation

表5 基坑开挖模拟分析时不同地层岩土参数指标取值<br/>Tab.5 Values of geotechnical parameters of different strata in foundation pit excavation simulation analysis

表5 基坑开挖模拟分析时不同地层岩土参数指标取值
Tab.5 Values of geotechnical parameters of different strata in foundation pit excavation simulation analysis

表6 模拟计算时岩土参数c、φ取值<br/>Tab.6 Values of geotechnical parameters c and φ during simulation calculation

表6 模拟计算时岩土参数c、φ取值
Tab.6 Values of geotechnical parameters c and φ during simulation calculation

图7 基坑深层水平位移监测点布置和断面选择图<br/>Fig.7 Layout of monitoring points and section selection for deep horizontal displacement of foundation pit

图7 基坑深层水平位移监测点布置和断面选择图
Fig.7 Layout of monitoring points and section selection for deep horizontal displacement of foundation pit

图8 滇池卫城站有限元二维基坑模型<br/>Fig.8 Finite element model of foundation

图8 滇池卫城站有限元二维基坑模型
Fig.8 Finite element model of foundation

图9 截面19开挖完成后水平方向位移云图<br/>Fig.9 Horizontal displacement nephogram of section 19 after excavation

图9 截面19开挖完成后水平方向位移云图
Fig.9 Horizontal displacement nephogram of section 19 after excavation

图10 基坑水平位移对比曲线<br/>Fig.10 Comparison curve of horizontal displacement of foundation pit

图10 基坑水平位移对比曲线
Fig.10 Comparison curve of horizontal displacement of foundation pit

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备注

引言

1 Bayes大样本方法确定的岩土参数

2 Bayes法岩土参数最小样本量的确定

3 滇池卫城深基坑开挖有限元分析

4 结论

期刊信息